Edexcel IAL Physics: Electric and Magnetic Fields — Revision Notes

Condensed for the final weeks. For the full explanation, use the Electric and Magnetic Fields study guide.

Electric fields

E = F / Q                      field strength, N C^-1 or V m^-1
E = Q / (4 pi epsilon0 r^2)    radial field
E = V / d                      uniform field between parallel plates
F = Q1 Q2 / (4 pi epsilon0 r^2)   Coulomb's law

Field strength is force per unit positive charge, so field lines run from positive to negative.

Radial fields obey an inverse square law; uniform fields do not vary with position. Applying the inverse square to parallel plates is a routine error.

A charged particle in a uniform field follows a parabolic path, exactly like a projectile in gravity — constant acceleration perpendicular to the initial velocity. The mathematics is identical, which is why the projectile method works.

Electric potential falls in the direction the field points, and field strength is (minus) the potential gradient. For a radial field, V = Q/4πε₀r. Equipotentials — surfaces of constant potential — are always perpendicular to field lines, for both radial and uniform fields.

Capacitance

C = Q / V              W = 1/2 QV = 1/2 CV^2 = Q^2 / 2C

Background — beyond the specification, not examinable (the only combination outcome in the whole specification is for resistors): capacitors combine the opposite way to resistors — in parallel, capacitance adds (C = C1 + C2); in series, reciprocals add (1/C = 1/C1 + 1/C2).

Energy stored is the area under a Q–V graph, which is why the ½ appears: the p.d. rises from zero to V as charge accumulates, so the average is V/2.

Discharge:

Q = Q0 e^(-t/RC)        time constant  tau = RC

After one time constant, the charge falls to 37% of its initial value. After 5RC it is effectively fully discharged. A larger RC gives slower discharge — larger capacitance stores more charge, larger resistance limits the current.

CORE PRACTICAL 11 uses an oscilloscope or data logger to display and analyse the p.d. across a capacitor as it charges and discharges through a resistor.

Worked example. A 220 μF capacitor is charged to 9.0 V, then discharged through a 47 kΩ resistor. Find the time constant and the p.d. after one time constant.

RC = (220 x 10^-6) x (47 x 10^3) = 10.34 s  (approx 10 s)
V = V0 x e^-1 = 9.0 x 0.368 = 3.3 V

Magnetic fields

F = B I L sin(theta)      force on a current-carrying conductor
F = B Q v sin(theta)      force on a moving charge

Fleming’s left-hand rule — First finger Field, seCond finger Current, thuMb Motion.

The force is zero when motion is parallel to the field and maximum when perpendicular.

A charged particle moving perpendicular to a uniform magnetic field travels in a circle, because the magnetic force is always perpendicular to the velocity — the definition of centripetal force. Setting BQv = mv²/r gives r = mv/BQ, the basis of mass spectrometry and particle accelerators.

Note this contrasts with an electric field, which gives a parabolic path because the force there has a fixed direction. That comparison is examined.

Electromagnetic induction

flux            phi = B A
flux linkage    N phi
Faraday:  induced e.m.f. = -d(N phi)/dt

Faraday’s law — the induced e.m.f. is proportional to the rate of change of flux linkage.

Lenz’s law — the induced current opposes the change producing it. The minus sign in Faraday’s law is Lenz’s law, and it follows from conservation of energy: if the induced effect assisted the change, energy would be created from nothing.

A transformer requires a.c. because only a continuously changing flux gives a rate of change and hence an induced e.m.f. Direct current produces constant flux and no induction.

Exam traps

• Applying the inverse square law to a uniform field.
• Forgetting the ½ in capacitor energy, or why it is there.
• Using the right hand for the motor effect.
• Saying a magnetic field gives a parabolic path — it gives a circular one.
• Omitting sin θ when the conductor is not perpendicular to the field.
• Drawing equipotentials parallel to field lines instead of perpendicular to them.

Self-test

1. Distinguish a radial from a uniform electric field.
2. (Background, not examinable.) How do capacitors combine in series and in parallel?
3. Why is there a factor of ½ in the energy stored on a capacitor?
4. Why does a magnetic field produce circular motion but an electric field a parabola?
5. State Lenz’s law and the principle it follows from.
6. How are equipotentials oriented relative to field lines?

Answers: 1. A radial field obeys an inverse square law and points towards or away from a point charge; a uniform field has constant strength and parallel field lines, as between charged parallel plates. 2. (Background, not examinable.) In parallel capacitances add; in series the reciprocals add — the opposite of resistors. 3. Energy is the area under the Q–V graph, and since p.d. rises linearly from zero to V, the average p.d. during charging is V/2. 4. The magnetic force is always perpendicular to the velocity, so it continuously changes direction, giving circular motion; the electric force has a fixed direction, giving constant acceleration in one direction and hence a parabola. 5. The induced current opposes the change producing it; it follows from conservation of energy. 6. Always perpendicular to the field lines, for both radial and uniform fields.